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Unformatted text preview: Strategy: a greedy algorithm that uses the largest
9coins first Making Change Inputs: Value N of the change to be returned An unlimited number of coins of values d1, d2,.., dk Output: the smallest possible set of coins that sums
to N Objective function? Smallest set Constraints on feasible solutions? Must sum to N Greedy rule: choose coin of largest value that is less
than N  Sum(coins chosen so far) Always optimal? Depends on set of coin values 10 Algorithm for making change This algorithm makes change for an amount A using coins of denominations denom[1] > denom[2] > ∙∙∙ > denom[n] = 1. Input P
arameters: denom, A Output P
arameters: None greedy_coin_change(denom, A) { i = 1 11 while (A > 0) { Making change proof Prove that the provided making change algorithm is
optimal for denominations 1, 5, and 10 Via induction, and on board > 12 Formal proof Formal
proof of the
change
problem Algorithm
7.1.1 is
what is
presented
two slides
previously 13 How would a failed proof work? Prove that the provided making change algorithm is
o...
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This note was uploaded on 02/25/2014 for the course CS 4102 taught by Professor Horton during the Spring '10 term at UVA.
 Spring '10
 HORTON
 Algorithms

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